For most of his career, Wheeler was a professor at Princeton University, which he joined in 1938, remaining until his retirement in 1976. At Princeton he supervised 46 PhDs, more than any other professor in the Princeton physics department. He was influential in mentoring a generation of physicists of the Golden Age of General Relativity, who made notable contributions to quantum mechanics and gravitation.

In 1933 Wheeler began dating Janette Hegner, who was taking graduate courses in history at Johns Hopkins.[11] Their relationship continued in New York the following year, after she began teaching at Rye Country Day School. They became engaged on their third date, but agreed to defer marriage until after he returned from Europe. They were married on June 10, 1935, five days after his return.[12] They had three children: Letitia, James English and Alison Wheeler.[13] Jobs were hard to come by during the Great Depression, but Arthur Ruark offered him a position as an assistant professor at the University of North Carolina at Chapel Hill, at an annual salary of $2,300, which was less than the $2,400 Janette was offered to stay at Rye Country Day School.[14][15]

Chapel Hill made Wheeler an associate professor in 1937, but he wanted to be able work more closely with the experts in particle physics.[16] He turned down an offer in 1938 of an associate professorship at Johns Hopkins University in favor of an assistant professorship at Princeton University. Although it was a lesser position, he felt that Princeton, which was building up its physics department, was a better career choice.[15] He remained a member of the faculty there until 1976.[13]

In a 1937 paper "On the Mathematical Description of Light Nuclei by the Method of Resonating Group Structure", Wheeler introduced the S-matrix – short for scattering matrix – "a unitary matrix of coefficients connecting the asymptotic behavior of an arbitrary particular solution [of the integral equations] with that of solutions of a standard form."[17][18]Werner Heisenberg subsequently developed the idea of the S-matrix in the 1940s. Due to the problematic divergences present in quantum field theory at that time, Heisenberg was motivated to isolate the essential features of the theory that would not be affected by future changes as the theory developed. In doing so he was led to introduce a unitary "characteristic" S-matrix, which became an important tool in particle physics.[17]

Bohr and Wheeler set to work applying the liquid drop model to explain the mechanism of nuclear fission.[22] As the experimental physicists studied fission, they uncovered puzzling results. George Placzek asked Bohr why uranium seemed to fission with both very fast and very slow neutrons. Walking to a meeting with Wheeler, Bohr had an insight that the fission at low energies was due to the uranium-235isotope, while at high energies it was mainly due to the far more abundant uranium-238 isotope.[23] They co-wrote two more papers on fission.[24][25] Their first paper appeared in the Physical Review on September 1, 1939, the day Germany invaded Poland, starting World War II in Europe.[26]

Considering the notion that positrons were electrons that were traveling backwards in time, he came up in 1940 with his one-electron universe postulate: that there was in fact only one electron, bouncing back and forth in time. His graduate student, Richard Feynman, found this hard to believe, but the idea that positrons were electrons traveling backwards in time intrigued him and Feynman incorporated the notion of the reversibility of time into his Feynman diagrams.[27]

After the United States Army Corps of Engineers took over the Manhattan Project, it gave responsibility for the detailed design and construction of the reactors to DuPont.[33] Wheeler became part of the DuPont design staff.[34] He worked closely with its engineers, commuting between Chicago and Wilmington, Delaware, where DuPont had its headquarters. He moved his family to Wilmington in March 1943.[35] DuPont's task was not just to build nuclear reactors, but an entire plutonium production complex at the Hanford Site in Washington.[36] As work progressed, Wheeler relocated his family again in July 1944, this time to Richland, Washington, where he worked in the scientific buildings known as the 300 area.[29][35]

Even before the Hanford Site started up the B Reactor, the first of its three reactors, on September 15, 1944, Wheeler had been concerned that some nuclear fission products might turn out to be nuclear poisons, the accumulation of which would impede the ongoing nuclear chain reaction by absorbing many of the thermal neutrons that were needed to continue a chain reaction.[37] In an April 1942 report, he predicted that this would reduce the reactivity by less than one percent so long as no fission product had a neutron capturecross section of more than 100,000 barns.[38] After the reactor unexpectedly shut down, and then just as unexpectedly restarted about fifteen hours later, he suspected iodine-135, with a half life of 6.6 hours, and its daughter product, xenon-135, which has a half life of 9.2 hours. Xenon-135 turned out to have a neutron capture cross-section of well over 2 million barns. The problem was corrected by adding additional fuel rods to burn out the poison.[39]

Wheeler had a personal reason for working on the Manhattan Project. His brother Joe, fighting in Italy, sent him a postcard with a simple message: "Hurry up".[40] It was already too late: Joe was killed in October 1944. "Here we were," Wheeler later wrote, "so close to creating a nuclear weapon to end the war. I couldn't stop thinking then, and haven't stopped thinking since, that the war could have been over in October 1944."[39] Joe left a widow and baby daughter, Mary Jo, who later married physicist James Hartle.[41]

In August 1945 Wheeler and his family returned to Princeton, where he resumed his academic career.[42] Working with Feynman, he explored the possibility of physics with particles, but not fields, and carried out theoretical studies of the muon with Jayme Tiomno,[43] resulting in a series of papers on the topic,[44][45] including a 1949 paper in which Tiomno and Wheeler introduced the "Tiomno Triangle", which related different forms of radioactive decay.[46] He also suggested the use of muons as a nuclear probe.[47] This paper, written in 1949 but not published in 1953, resulted in a series of measurements of the Chang radiation emitted by muons. Muons are a component of cosmic rays, and Wheeler became the founder and first director of Princeton's Cosmic Rays Laboratory, which received a substantial grant of $375,000 from the Office of Naval Research in 1948.[48] He received a Guggenheim Fellowship in 1946,[49] which allowed him to spend the 1949–50 academic year in Paris.[50]

At Los Alamos, Wheeler and his family moved into the house on "Bathtub Row" that had been occupied by Robert Oppenheimer and his family during the war.[55] In 1950 there was no practical design for a hydrogen bomb. Calculations by Stan Ulam and others showed that Teller's "Classical Super" would not work. Teller and Wheeler created a new design known as "Alarm Clock", but it was not a true thermonuclear weapon. Not until January 1951 did Ulam come up with a workable design.[56]

In 1951 Wheeler obtained permission from Bradbury to set up a branch office of the Los Alamos laboratory at Princeton, known as Project Matterhorn, which had two parts. Matterhorn S (for stellarator, another name coined by Wheeler), under Lyman Spitzer, investigated nuclear fusion as a power source. Matterhorn B (for bomb), under Wheeler, engaged in nuclear weapons research. Senior scientists remained disinterested and aloof from the project, so he staffed it with young graduate and post-doctoral students.[57] In January 1953 he was involved in a security breach when he lost a highly classified paper on lithium-6 and the hydrogen bomb design during an overnight train trip. This resulted in Wheeler being given an official reprimand.[58] Matterhorn B's efforts were crowned by the success of the Ivy Mike nuclear test at Enewetak Atoll in the Pacific, on November 1, 1953,[59][57] which Wheeler witnessed. The yield of the Ivy Mike "Sausage" device was reckoned at 10.4 megatons of TNT (44 PJ), about 30 percent higher than Matterhorn B had estimated.[60] Matterhorn B was discontinued, but Matterhorn S endures as the Princeton Plasma Physics Laboratory.[57]

After concluding his Matterhorn Project work, Wheeler resumed his academic career. In a 1955 paper he theoretically investigated the geon, an electromagnetic or gravitational wave that is held together in a confined region by the attraction of its own field. He coined the name as a contraction of "gravitational electromagnetic entity."[61] He found that the smallest geon was a toroid the size of the Sun, but millions of times heavier.[62] While working on mathematical extensions to Einstein's Theory of General Relativity in 1957, Wheeler introduced the concept and word wormhole to describe hypothetical "tunnels" in space-time. Bohr asked if they are stable and further research by Wheeler determined that they are not.[63][64]

Alluding to Wheeler's "mass without mass", the festschrift honoring his 60th birthday was titled Magic Without Magic: John Archibald Wheeler: A Collection of Essays in Honor of his Sixtieth Birthday (1972). His writing style could also attract parodies, including one by "John Archibald Wyler" that was affectionately published by a relativity journal.[72][73] Wheeler wrote Geometrodynamics (1962), and teamed up with Edwin F. Taylor to write Spacetime Physics (1966) and Scouting Black Holes (1996). With Kent Harrison, Kip Thorne and Masami Wakano he wrote Gravitation Theory and Gravitational Collapse (1954). This led to the voluminous general relativity textbook Gravitation (1973), co-written with Misner and Thorne. Its timely appearance during the golden age of general relativity and its comprehensiveness made it an influential relativity textbook for a generation.[74]

Looking back on Wheeler’s 10 years at Texas, many quantum information scientists now regard him, along with IBM’s Rolf Landauer, as a grandfather of their field. That, however, was not because Wheeler produced seminal re-search papers on quantum information. He did not—with one major exception, his delayed-choice experiment. Rather, his role was to inspire by asking deep questions from a radical conservative viewpoint and, through his questions, to stimulate others’ research and discovery.[76]

Wheeler's delayed choice experiment is actually several thought experiments in quantum physics that he proposed, with the most prominent among them appearing in 1978 and 1984. These experiments are attempts to decide whether light somehow "senses" the experimental apparatus in the double-slit experiment it will travel through and adjusts its behavior to fit by assuming the appropriate determinate state for it, or whether light remains in an indeterminate state, neither wave nor particle, and responds to the "questions" asked of it by responding in either a wave-consistent manner or a particle-consistent manner depending on the experimental arrangements that ask these "questions".[77]

In 1990 Wheeler suggested that information is fundamental to the physics of the universe. According to this "it from bit" doctrine, all things physical are information-theoretic in origin.

Wheeler: It from bit. Otherwise put, every "it" — every particle, every field of force, even the space-time continuum itself — derives its function, its meaning, its very existence entirely — even if in some contexts indirectly — from the apparatus-elicited answers to yes-or-no questions, binary choices, bits. "It from bit" symbolizes the idea that every item of the physical world has at bottom — a very deep bottom, in most instances — an immaterial source and explanation; that which we call reality arises in the last analysis from the posing of yes-or-no questions and the registering of equipment-evoked responses; in short, that all things physical are information-theoretic in origin and that this is a participatory universe.[83]

Wheeler speculated that reality is created by observers in the universe. "How does something arise from nothing?", he asked about the existence of space and time.[84] He also coined the term "Participatory Anthropic Principle" (PAP), a version of a Strong Anthropic Principle. From a transcript of a radio interview on "The anthropic universe":

Wheeler: We are participators in bringing into being not only the near and here but the far away and long ago. We are in this sense, participators in bringing about something of the universe in the distant past and if we have one explanation for what's happening in the distant past why should we need more?Martin Redfern: Many don't agree with John Wheeler, but if he's right then we and presumably other conscious observers throughout the universe, are the creators — or at least the minds that make the universe manifest.[85]